Is it realistic that I can find a brokerage to hang my license with that will be hands-off enough to let me "do my own thing", but will still provide training and enough support to make me comfortable representing myself for my first few transactions?

He leaves you hanging, so what?

Join a professional organization and hang out with like minded individuals.

I do both, you are going to want to hang your license at a brokerage that will allow for you to do it 

Beyond being where your audience is likely hanging out, the business features built into Facebook are perfect for real estate businesses.

If you hang around the real estate investing community for any amount of time, you are going to hear a lot about investing through syndications.

Just hang up, and move on. 

Instead you're going to have a whole lot of inventory just get removed from the market or never make to market in the first place, and the owners will either remain in their 3.5% homes or they'll find ways to hang on to the home in the meantime, such as turning short term rentals into long term rentals (I saw this when I was looking in Four Corners, where a lot of the vacation homes had been turned into rentals while the owners waited for property values to recover).

The cost of getting your license is pretty standard but hanging your license at a sponsoring brokerage with the various commission splits, office fees or flat fee structure is different from location to location.

Hang in there.